\ jdZddlZddlZddlmZdZGdde Z Gdde Z Gd d e Z Gd d e Z Gd de ZdS)a`Matrix and Vector math. This module provides Vector and Matrix objects, include Vec2, Vec3, Vec4, Mat3 and Mat4. Most common operations are supported, and many helper methods are included for rotating, scaling, and transforming. The :py:class:`~pyglet.matrix.Mat4` includes class methods for creating orthographic and perspective projection matrixes. N)mulc>tt|||SN)maxmin)nummin_valmax_vals E/DATA/AppData/hermes/venv/lib/python3.11/site-packages/pyglet/math.pyclampr 2s s3  ' * **c eZdZdZfdZedZedZedZ edZ edZ dZ d Z d Zd Zd Zd ZddZdZdZdZdZdZdZdZdZdZdZdZdZdZxZ S)Vec2aA two dimensional vector represented as an X Y coordinate pair. :parameters: `x` : int or float : The X coordinate of the vector. `y` : int or float : The Y coordinate of the vector. Vectors must be created with either 0 or 2 values. If no arguments are provided a vector with the coordinates 0, 0 is created. Vectors are stored as a tuple and therefore immutable and cannot be modified directly ct|dvs Jdtt|pdS)N)rz*0 or 2 values are required for Vec2 types.)rr)lensuper__new__rclsargs __class__s r rz Vec2.__new__Ds?4yyF"""$P"""wwtT^V444r cvt|tj|z|tj|zS)aWCreate a new vector from the given polar coodinates. :parameters: `mag` : int or float : The magnitude of the vector. `angle` : int or float : The angle of the vector in radians. :returns: A new vector with the given angle and magnitude. :rtype: Vec2 )r_mathcossin)magangles r from_polarzVec2.from_polarHs2C%)E***C%)E2B2B,BCCCr c|dSz>The X coordinate of the vector. :type: float rselfs r xzVec2.xW Awr c|dSz>The Y coordinate of the vector. :type: float r"r#s r yzVec2.y_r&r cDtj|d|dS)zBThe angle of the vector in radians. :type: float r)r)ratan2r#s r headingz Vec2.headinggs {47DG,,,r c*|SzThe magnitude, or length of the vector. The distance between the coordinates and the origin. Alias of abs(self). :type: float __abs__r#s r rzVec2.mago||~~r c^t|d|dz|d|dzSNrr)rr$others r __add__z Vec2.__add__y,DGeAh&Q%((:;;;r c^t|d|dz |d|dz Sr4r5r6s r __sub__z Vec2.__sub__|r9r c^t|d|dz|d|dzSr4r5r6s r __mul__z Vec2.__mul__r9r c^t|d|dz |d|dz Sr4r5r6s r __truediv__zVec2.__truediv__r9r cTtj|ddz|ddzzSNrrr)rsqrtr#s r r1z Vec2.__abs__s'z$q'Q,aA5666r c>t|d |d Sr4r5r#s r __neg__z Vec2.__neg__sT!WHtAwh'''r Nc.tfd|DS)Nc38K|]}t|VdSrround.0vndigitss r z!Vec2.__round__..-66AeAw''666666r r5r$rMs `r __round__zVec2.__round__#666666677r c<|dkr|S||Sz;Reverse add. Required for functionality with sum() rr8r6s r __radd__z Vec2.__radd__$ A::K<<&& &r cP||S)a4Create a new Vector of the given magnitude by normalizing, then scaling the vector. The heading remains unchanged. :parameters: `magnitude` : int or float : The magnitude of the new vector. :returns: A new vector with the magnitude. :rtype: Vec2  normalizescaler$ magnitudes r from_magnitudezVec2.from_magnitude"~~%%i000r c|}t|tj|z|tj|zS)a3Create a new vector of the same magnitude with the given heading. I.e. Rotate the vector to the heading. :parameters: `heading` : int or float : The angle of the new vector in radians. :returns: A new vector with the given heading. :rtype: Vec2 )r1rrrr)r$r-rs r from_headingzVec2.from_headings?llnnC%)G,,,cEIg4F4F.FGGGr cl|ddz|ddzz||zkr||S|S)a#Limit the magnitude of the vector to the value used for the max parameter. :parameters: `max` : int or float : The maximum magnitude for the vector. :returns: Either self or a new vector with the maximum magnitude. :rtype: Vec2 rrr)r^r$rs r limitz Vec2.limitsA 7a<$q'Q, &s 2 2&&s++ + r ct|d||d|dz zz|d||d|dz zzS)aCreate a new vector lineraly interpolated between this vector and another vector. :parameters: `other` : Vec2 : The vector to be linerly interpolated to. `alpha` : float or int : The amount of interpolation. Some value between 0.0 (this vector) and 1.0 (other vector). 0.5 is halfway inbetween. :returns: A new interpolated vector. :rtype: Vec2 rr)r5r$r7alphas r lerpz Vec2.lerpsQDGua47(:;<Gua47(:;<>> >r cFt|d|z|d|zS)zMultiply the vector by a scalar value. :parameters: `value` : int or float : The ammount to be scaled by :returns: A new vector scaled by the value. :rtype: Vec2 rr)r5r$values r r[z Vec2.scales$DGeOT!Wu_555r c|j}|j}t|tj||zz|tj||zzS)a Create a new Vector rotated by the angle. The magnitude remains unchanged. :parameters: `angle` : int or float : The angle to rotate by :returns: A new rotated vector of the same magnitude. :rtype: Vec2 )rr-rrrr)r$rrr-s r rotatez Vec2.rotatesHh,C%)GeO444cEIgemzE!HtAw.14%(T!W:LQR9RSTTTr cv|}|r"t|d|z |d|z S|S)zNormalize the vector to have a magnitude of 1. i.e. make it a unit vector. :returns: A unit vector with the same heading. :rtype: Vec2 rr))r1rr$ds r rZzVec2.normalizes> LLNN  2Q! T!Wq[11 1 r cvtt|d||t|d||S)a`Restrict the value of the X and Y components of the vector to be within the given values. :parameters: `min_val` : int or float : The minimum value `max_val` : int or float : The maximum value :returns: A new vector with clamped X and Y components. :rtype: Vec2 rr))rr r$r r s r r z Vec2.clamps4E$q'7G44eDGWg6V6VWWWr cH|d|dz|d|dzzS)zCalculate the dot product of this vector and another 2D vector. :parameters: `other` : Vec2 : The other vector. :returns: The dot product of the two vectors. :rtype: float rr)r"r6s r dotzVec2.dot s)Awq!DGeAh$666r c tttdt |}|fd|DS#t $r!t djjd|dwxYw)Nrc3NK|]}d|V dS)xyNindexrKcr$s r rNz#Vec2.__getattr__..s2BBqtDJJqMM2BBBBBBr '' object has no attribute ' rVec3Vec4getr ExceptionAttributeErrorr__name__r$attrs vec_classs` r __getattr__zVec2.__getattr__s c Td3377E CCI9BBBBEBBBC C c c c !aT^%>>" 6 6 6 V V V U U U    X X X 7 7 7ccc-------r rceZdZdZfdZedZedZedZedZ dZ dZ d Z d Z d Zd ZddZdZdZdZdZdZdZdZdZdZdZdZdZxZS)raA three dimensional vector represented as a X Y Z coordinates. :parameters: `x` : int or float : The X coordinate of the vector. `y` : int or float : The Y coordinate of the vector. `z` : int or float : The Z coordinate of the vector. 3D Vectors must be created with either 0 or 3 values. If no arguments are provided a vector with the coordinates 0, 0, 0 is created. Vectors are stored as a tuple and therefore immutable and cannot be modified directly ct|dvs Jdtt|pdS)N)rrzz*0 or 3 values are required for Vec3 types.)rrr)rrrrrs r rz Vec3.__new__5s@4yyF"""$P"""wwtT%6Y777r c|dSr!r"r#s r r%zVec3.x9r&r c|dSr(r"r#s r r*zVec3.yAr&r c|dS)z>The Z coordinate of the vector. :type: float rr"r#s r zzVec3.zIr&r c*|Sr/r0r#s r rzVec3.magQr2r c~t|d|dz|d|dz|d|dzSNrr)rrr6s r r8z Vec3.__add__[;DGeAh&Q%((:DGeAh.nrOr rrPs `r rQzVec3.__round__mrRr c<|dkr|S||SrTrUr6s r rVz Vec3.__radd__prWr cP||S)a5Create a new Vector of the given magnitude by normalizing, then scaling the vector. The rotation remains unchanged. :parameters: `magnitude` : int or float : The magnitude of the new vector. :returns: A new vector with the magnitude. :rtype: Vec3 rYr\s r r^zVec3.from_magnitudexr_r c|ddz|ddzz|ddzz||z|zkr||S|S)a#Limit the magnitude of the vector to the value used for the max parameter. :parameters: `max` : int or float : The maximum magnitude for the vector. :returns: Either self or a new vector with the maximum magnitude. :rtype: Vec3 rrr)rcrds r rez Vec3.limitsR 7a<$q'Q, &a1 4sSy3 F F&&s++ + r ct|d|dz|d|dzz |d|dz|d|dzz |d|dz|d|dzz S)zCalculate the cross product of this vector and another 3D vector. :parameters: `other` : Vec3 : The other vector. :returns: The cross product of the two vectors. :rtype: float r)rrrr6s r crossz Vec3.crosss~T!WuQx'DGeAh,>?!WuQx'DGeAh,>?!WuQx'DGeAh,>?AA Ar cl|d|dz|d|dzz|d|dzzS)zCalculate the dot product of this vector and another 3D vector. :parameters: `other` : Vec3 : The other vector. :returns: The dot product of the two vectors. :rtype: float rr)rr"r6s r rwzVec3.dots;Awq!DGeAh$66a589KKKr c t|d||d|dz zz|d||d|dz zz|d||d|dz zzS)aCreate a new vector lineraly interpolated between this vector and another vector. :parameters: `other` : Vec3 : The vector to be linerly interpolated to. `alpha` : float or int : The amount of interpolation. Some value between 0.0 (this vector) and 1.0 (other vector). 0.5 is halfway inbetween. :returns: A new interpolated vector. :rtype: Vec3 rr)rrrgs r riz Vec3.lerpsoDGua47(:;<Gua47(:;<Gua47(:;<>> >r cZt|d|z|d|z|d|zS)zMultiply the vector by a scalar value. :parameters: `value` : int or float : The ammount to be scaled by :returns: A new vector scaled by the value. :rtype: Vec3 rr)rrrks r r[z Vec3.scales.DGeOT!Wu_d1goFFFr ctj|d|dz dz|d|dz dzz|d|dz dzzS)zCalculate the distance between this vector and another 3D vector. :parameters: `other` : Vec3 : The other vector :returns: The distance between the two vectors. :rtype: float rrr)rBr6s r rpz Vec3.distances`zE!HtAw.14!!HtAw.146!!HtAw.14677 7r c|}|r,t|d|z |d|z |d|z S|S)zNormalize the vector to have a magnitude of 1. i.e. make it a unit vector. :returns: A unit vector with the same rotation. :rtype: Vec3 rr)r)r1rrrs r rZzVec3.normalizesH LLNN  ?Q! T!Wq[$q'A+>> > r c tt|d||t|d||t|d||S)agRestrict the value of the X, Y and Z components of the vector to be within the given values. :parameters: `min_val` : int or float : The minimum value `max_val` : int or float : The maximum value :returns: A new vector with clamped X, Y and Z components. :rtype: Vec3 rr)r)rr rus r r z Vec3.clampsNE$q'7G44$q'7G44$q'7G4466 6r c tttdt |}|fd|DS#t $r!t djjd|dwxYw)Nryc3NK|]}d|V dS)xyzNr~rs r rNz#Vec3.__getattr__..s2CCtEKKNN3CCCCCCr rrrrs` r rzVec3.__getattr__s c Td3377E CCI9CCCCUCCCD D c c c !aT^%d|dd|dd|ddS)NzVec3(rrr)rrr"r#s r rz Vec3.__repr__s/7tAw77$q'77T!W7777r r)rrrrrrr%r*rrr8r;r=r?r1rErQrVr^rerrwrir[rprZr rrrrs@r rr%s  88888XXXXPPPPPPPPPPPPFFF2228888''' 1 1 1    A A A L L L>>>$ G G G 7 7 7   666 ccc8888888r rceZdZfdZedZedZedZedZdZ dZ dZ d Z d Z d Zdd ZdZdZdZdZdZdZdZdZdZxZS)rct|dvs Jdtt|pdS)N)rr{z*0 or 4 values are required for Vec4 types.)rrrr)rrrrrs r rz Vec4.__new__s@4yyF"""$P"""wwtT%9\:::r c|dSNrr"r#s r r%zVec4.x Awr c|dS)Nr)r"r#s r r*zVec4.y rr c|dS)Nrr"r#s r rzVec4.z rr c|dS)Nrzr"r#s r wzVec4.wrr ct|d|dz|d|dz|d|dz|d|dzSNrr)rrzrr6s r r8z Vec4.__add__PDGeAh&Q%((:DGeAh.(rOr rrPs `r rQzVec4.__round__'rRr c<|dkr|S||SrrUr6s r rVz Vec4.__radd__*s" A::K<<&& &r c t|d||d|dz zz|d||d|dz zz|d||d|dz zz|d||d|dz zzSrrrgs r riz Vec4.lerp0sDGua47(:;<Gua47(:;<Gua47(:;<Gua47(:;<>> >r cnt|d|z|d|z|d|z|d|zSrrrks r r[z Vec4.scale6s7DGeOT!Wu_d1gotAwQVWWWr ctj|d|dz dz|d|dz dzz|d|dz dzz|d|dz dzzSrrBr6s r rpz Vec4.distance9szzE!HtAw.14!!HtAw.146!!HtAw.146"!HtAw.14677 7r c|}|r6t|d|z |d|z |d|z |d|z S|Sr)r1rrrs r rZzVec4.normalize?sQ LLNN  LQ! T!Wq[$q'A+tAw{KK K r c tt|d||t|d||t|d||t|d||Sr)rr rus r r z Vec4.clampEs_E$q'7G44$q'7G44$q'7G44$q'7G4466 6r c|d|dz|d|dzz|d|dzz|d|dzzSrr"r6s r rwzVec4.dotKsOAwq!DGeAh$66a589KKdSTgX]^_X`N```r c tttdt |}|fd|DS#t $r!t djjd|dwxYw)Nryc3NK|]}d|V dS)xyzwNr~rs r rNz#Vec4.__getattr__..Rs2DDtFLLOO4DDDDDDr rrrrs` r rzVec4.__getattr__Ns c Td3377E CCI9DDDDeDDDE E c c c !aT^%>> XXX777  666 aaacccCCCCCCCr rceZdZdZddfd ZdedefdZded efd Zd efd Zdedefd Z ddZ ddZ dZ ddZ dddZdZddZdefdZxZS)Mat3zA 3x3 Matrix class `Mat3` is an immutable 3x3 Matrix, including most common operators. Matrix multiplication must be performed using the "@" operator. Nreturnc|t|dks Jdtt|pdS)aCreate a 3x3 Matrix A Mat3 can be created with a list or tuple of 9 values. If no values are provided, an "identity matrix" will be created (1.0 on the main diagonal). Matrix objects are immutable, so all operations return a new Mat3 object. :Parameters: `values` : tuple of float or int A tuple or list containing 9 floats or ints. N zA 3x3 Matrix requires 9 values) ?rrrrrrr)rrrrrvaluesrs r rz Mat3.__new__bsT~V!1!1!13S!1!11wwtV&?0?@@ @r sxsyc *|d|z dddd|z ddddf zSNrrr"r$rrs r r[z Mat3.scaless(sRxc3b#sCMMMr txtyc  |dddddd| |df zSrr")r$rrs r translatezMat3.translatevs"sCc3bS"cBBBr phic tjtj|}tjtj|}|||d| |ddddf zSNrr)rrradiansr)r$rsrs r rnz Mat3.rotateysT IemC(( ) ) IemC(( ) )q!S1"ac3<<.*==DAq!a%======r rrtuplezipr6s r r8z Mat3.__add__sK5zzQ BE==Ce,<,<=====>>>r c t|dks Jdttdt||DS)Nrz'Can only subtract from other Mat3 typesc3&K|] \}}||z V dSrr"rs r rNzMat3.__sub__..rr rr6s r r;z Mat3.__sub__sK5zzQ IE==Ce,<,<=====>>>r c|Srr"r#s r __pos__z Mat3.__pos__ r cNttd|DS)Nc3K|]}| VdSrr"rKrLs r rNzMat3.__neg__..$++1"++++++r rrr#s r rEz Mat3.__neg__'E++d+++++,,,r cTttfd|DS)Nc38K|]}t|VdSrrHrJs r rNz!Mat3.__round__..-::%7++::::::r rrPs `r rQzMat3.__round__.E::::T:::::;;;r c tdNz4Please use the @ operator for Matrix multiplication.NotImplementedErrorr6s r r=z Mat3.__mul__!"XYYYr ct|dvs Jdt|tur|ddd}|ddd}|ddd}ttt t ||tt t ||tt t ||S|dd}|dd}|dd}|ddd}|ddd}|ddd}t tt t ||tt t ||tt t ||tt t ||tt t ||tt t ||tt t ||tt t ||tt t ||f S) N)rzrz)Can only multiply with Mat3 or Vec3 typesrrzr)rr)rtypersummap_mulr)r$r7c0c1c2r0r1r2s r __matmul__zMat3.__matmul__s5zzV###%P### ;;$  addBaddBaddBCb%0011Cb%0011Cb%001133 3 !A#Y !A#Y !A#Y 14a4[ 14a4[ 14a4[ST2r**++T2r**++T2r**++T2r**++T2r**++T2r**++T2r**++T2r**++T2r**++ - . . .r c^|jj|ddd|ddd|ddS)Nrrz rrrrr#s r rz Mat3.__repr__sC.)X4!9XXD1IXXTRSTURUYXXXr r)rr)rrrrrfloatr[rrnrr8r;rrErQr=rstrrrrs@r rrZs@@@@@@@"NN5NNNNCECuCCCC=%==== BB5BBBB????????----<<<<<ZZZ . . . .DY#YYYYYYYYr rc eZdZdZd"d#fd Zed#dZed$d#dZededdfd Z ed e deddfd Z ed ed eddfdZ ededed eddfdZ defdZdefdZdeddfdZdeddfdZd e deddfdZd#dZd#dZd#dZdZd#dZd#dZd"d#dZdZd#d Zdefd!ZxZS)%Mat4a A 4x4 Matrix class `Mat4` is an immutable 4x4 Matrix, including most common operators. Matrix multiplication must be performed using the "@" operator. Class methods are available for creating orthogonal and perspective projections matrixes. Nrc|t|dks Jdtt|pdS)aCreate a 4x4 Matrix A Matrix can be created with a list or tuple of 16 values. If no values are provided, an "identity matrix" will be created (1.0 on the main diagonal). Matrix objects are immutable, so all operations return a new Mat4 object. :Parameters: `values` : tuple of float or int A tuple or list containing 16 floats or ints. NzA 4x4 Matrix requires 16 values)rrrrrrrrrrrrrrrr)rrrr$rs r rz Mat4.__new__sV~V!2!2!24U!2!22wwtV&D0DEE Er c||z }||z }||z } d|z } d|z } d| z } ||z |z } ||z |z }||z | z }|| dddd| dddd| d| ||dfS)z-Create a Mat4 orthographic projection matrix.g@rrr")rleftrightbottomtopz_nearz_farwidthheightdepthrrszrrtzs r orthogonal_projectionzMat4.orthogonal_projections v 5[ 6\ E6\t|_u $V|_v %v~  &sBS#S#b#B%&& &r <c ||z }||z } || z } |tj|tjzdz z} | } | } | | z }| | z } ||z }||z |z }d|z|z|z }d|z|z }|| z }d|z| z }||dddd|dddd|ddd|dfS)z,Create a Mat4 perspective projection matrix.ihrr)rtanpi)rr(r)r*r+r,r-fovr.r/aspectxy_maxy_minx_minr0qqnrhs r perspective_projectionzMat4.perspective_projections v%)C%(NS$8999%fn  % %Z& 5 ( J  J J sAq!QaAaBaQ !! !r vectorc\|dddddddddddd|d|d|ddfS)zCreate a translaton matrix from a Vec3. :Parameters: `vector` : A `Vec3`, or 3 component tuple of float or int Vec3 or tuple with x, y and z translaton values rrrr)rr")rrCs r from_translationzMat4.from_translationsLsCc3c3c31Ivay&)S:;; ;r rc>|||S)zCreate a rotation matrix from an angle and Vec3. :Parameters: `angle` : A `float` `vector` : A `Vec3`, or 3 component tuple of float or int Vec3 or tuple with x, y and z translaton values )rn)rrrCs r from_rotationzMat4.from_rotationssuu||E6***r directionupcV|}||}||}||j|j|jd|j|j|jd|j|j|jdddddfSr)rZ cross_productr%r*r)rrHrIvec_zvec_xvec_ys r look_at_directionzMat4.look_at_directions##%%''++5577''..88::sEGUWegsGUWegsGUWegsc3()) )r positiontargetc||z }|||}||}||zSr)rOrEnegate)rrPrQrIrHdirection_mat4 position_mat4s r look_atz Mat4.look_at(sIX% ..y"==,,X__->->??  --r rc(||dz|dzdzS)zGet a specific row as a tuple.r{r"r$rs r rowzMat4.row/sE!GE!GAI%&&r c||ddS)z!Get a specific column as a tuple.Nr{r"rXs r columnz Mat4.column3sEH1H~r ct|}|dxx|dzcc<|dxx|dzcc<|dxx|dzcc<t|S)z&Get a scale Matrix on x, y, or z axis.rr) r)listr$)r$rCtemps r r[z Mat4.scale7sgDzz Q6!9 Q6!9 RF1IDzzr cbt|tddddddddddddg |dRzS)z.Get a translate Matrix along x, y, and z axis.r)rr$)r$rCs r rzMat4.translate?sADzzD!Q1aAq!Q1!Qv!Qq!Q!QRRRRr ctd|Ds Jd|\}}}tj|}tj|}d|z }||z||z||z} } } || |zz} d| |zz||zz} d| |zz||zz }d| |zz||zz }|| |zz}d| |zz||zz}d| |zz||zz}d| |zz||zz }|| |zz}t |t | | |d|||d|||dddddfzS)z)Get a rotation Matrix on x, y, or z axis.c3<K|]}t|dkVdS)r)N)abs)rKns r rNzMat4.rotate..Es,//13q66Q;//////r zvector must be normalized (<=1)r)r)allrrrr$)r$rrCr%r*rrrttemp_xtemp_ytemp_zrarbrcrerfrgrirjrks r rnz Mat4.rotateCsc///////RR1RRR/1a Ie   Ie   E!"QAq1u !^ !^a!e # !^a!e # !^a!e # !^ !^a!e # !^a!e # !^a!e # !^DzzD"b"aRQBAqRSUVXY!Z[[[[r czt|ddd|dddz|dddz|dddzS)zGet a tranpose of this Matrix.rNr{r)rrzrbr#s r transposezMat4.transpose]sGDAJadd+d14a4j841:EFFFr c t|dks Jdttdt||DS)Nr&z Can only add to other Mat4 typesc3&K|] \}}||zV dSrr"rs r rNzMat4.__add__..crr rr$rrr6s r r8z Mat4.__add__asQ5zzR!CE==Ce,<,<=====>>>r c t|dks Jdttdt||DS)Nr&z'Can only subtract from other Mat4 typesc3&K|] \}}||z V dSrr"rs r rNzMat4.__sub__..grr ryr6s r r;z Mat4.__sub__esQ5zzR!JE==Ce,<,<=====>>>r c|Srr"r#s r rz Mat4.__pos__irr cNttd|DS)Nc3K|]}| VdSrr"rs r rNzMat4.__neg__..mrr r$rr#s r rEz Mat4.__neg__lrr cZ |d|dz|d|dzz }|d|dz|d|dzz }|d|dz|d|dzz }|d|dz|d|dzz }|d|dz|d|dzz }|d|dz|d|dzz }|d |dz|d |dzz }|d |dz|d |dzz }|d |dz|d |dzz } |d |dz|d |dzz } |d |dz|d |dzz } |d |dz|d |dzz } |d |dz|d |dzz } |d |dz|d |dzz }|d |dz|d |dzz }|d |dz|d |dzz }|d |dz|d |dzz }|d |dz|d |dzz }|d |d |z|d |zz |d |zzz|d|d |z|d |zz |d |zzzz |d|d |z|d |zz |d |zzzz|d|d |z|d |zz |d |zzzz }|d krtjd|Sd|z }| }t||d |z|d |zz |d |zzz||d|z|d|zz |d|zzz||d|z|d|zz |d| zzz||d| z|d| zz |d| zzz||d |z|d |zz |d |zzz||d |z|d|zz |d|zzz||d |z|d| zz |d|zzz||d | z|d|zz |d|zzz||d |z|d |zz |d |zzz||d |z|d|zz |d|zzz||d |z|d| zz |d|zzz||d | z|d|zz |d|zzz||d |z|d |zz |d |zzz||d |z|d|zz |d|zzz||d | z|d|zz |d|zzz||d | z|d|zz |d|zzzfS)Nr^ r  rr]r{rr)rrzz.Unable to calculate inverse of singular Matrix) _warningswarnr$)r$abrrsefgrAijklmrfrpr?rdetpdetndets r __invert__zMat4.__invert__osC HtBx $r(T"X"5 5 Gd2h bDH!4 4 Gd2h bDH!4 4 Gd2h bDH!4 4 Gd2h bDH!4 4 Gd2h a48!3 3 Gd2h a48!3 3 Gd2h a48!3 3 Gd2h a48!3 3 Gd2h a48!3 3 Gd2h a47!2 2 Gd2h a47!2 2 Gd2h a48!3 3 Gd2h a48!3 3 Gd2h a47!2 2 Gd2h a47!2 2 Gd2h a48!3 3 Gd1g Q$q' 1 1Aw$q'A+Q! 3d1gkABaDGaK$q'A+5Q! CDEaDGaK$q'A+5Q! CDEaDGaK$q'A+5Q! 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